The exotic substances have exotic properties. One class of such substances is geometrically frustrated magnets, where correlated spins reside in the sites of triangular or kagomé lattice. In some ...cases, such magnet would not have long-range magnetic order. Rather, its spins tend to form kind of pairs, called valence bonds. At
T
→
0
these highly entangled quantum objects condense in the form of a liquid, called quantum spin liquid (QSL). The observation of a gapless QSL in actual materials is of fundamental significance both theoretically and technologically, as it could open a path to creation of topologically protected states for quantum information processing and computation. In the present review, we consider QSL formed by spinons that are chargeless fermionic quasiparticles with spin 1/2, filling the Fermi sphere up to the Fermi momentum
p
F
. We expose a state of the art in the theoretical and experimental investigations of the thermodynamic, relaxation, transport, optical and scaling properties of geometrically frustrated magnets with QSL. We show how different theoretical approaches and that based on so-called fermion condensation concept among them, permit to describe the multitude of experimental results regarding the thermodynamic and transport properties of QSL in geometrically frustrated magnets like herbertsmithite
ZnCu
3
(
OH
)
6
Cl
2
, the organic insulators
EtMe
3
Sb
Pd(dmit)
2
2
and
κ
-
(
BEDT-TTF
)
2
Cu
2
(
CN
)
3
, quasi-one-dimensional spin liquid in the
Cu
(
C
4
H
4
N
2
)
(
NO
3
)
2
insulator and QSL formed in two-dimensional
3
He
. Our theoretical results are in good agreement with experimental facts, while predictions, elucidating the existence of gapless QSL in magnets, still await their experimental confirmation.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Extraordinary new materials named quasicrystals and characterized by noncrystallographic rotational symmetry and quasiperiodic translational properties have attracted scrutiny. Study of quasicrystals ...may shed light on the most basic notions related to the quantum critical state observed in heavy-fermion metals. We show that the electronic system of some quasicrystals is located at the fermion condensation quantum phase transition without tuning. In that case the quasicrystals possess the quantum critical state with the non-Fermi-liquid behavior which in magnetic fields transforms into the Landau Fermi-liquid one. Remarkably, the quantum critical state is robust despite the strong disorder experienced by the electrons. We also demonstrate for the first time that quasicrystals exhibit the typical scaling behavior of their thermodynamic properties such as the magnetic susceptibility, and belong to the famous family of heavy-fermion metals. Our calculated thermodynamic properties are in good agreement with recent experimental observations.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
We show that a quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors ...represented by La
Sr
CuO
, whose superconductivity features differ from what is predicted by the classical Bardeen-Cooper-Schrieffer theory. This observation can open avenues for chemical preparation of high-T
materials. We demonstrate that (1) at temperature T = 0, the superfluid density n
turns out to be considerably smaller than the total electron density; (2) the critical temperature T
is controlled by n
rather than by doping, and is a linear function of the n
; (3) at T > T
the resistivity ρ(T) varies linearly with temperature, ρ(T) ∝ αT, where α diminishes with T
→ 0, whereas in the normal (non superconducting) region induced by overdoping, T
= 0, and ρ(T) ∝ T
. Our results are in good agreement with recent experimental observations.
In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example ...here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits the NFL properties, so that the C symmetry breaks down, making the differential tunneling conductivity to be an asymmetric function of the bias voltage V. This asymmetry does not take place in normal metals, where Landau Fermi liquid (LFL) theory holds. Under the application of magnetic field, a heavy fermion metal transits to the LFL state, and σ(V) becomes symmetric function of V. These findings are in good agreement with experimental observations. We suggest that the same topological FCQPT underlies the baryon asymmetry in the Universe. We demonstrate that the most fundamental features of the nature are defined by its topological and symmetry properties.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems ...and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-
T
c
superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition. We emphasize that so-called Planckian limit, widely used to explain the above universal scattering rate, may occur accidentally as in conventional metals its experimental manifestations (e.g., scattering rate at room and higher temperatures) are indistinguishable from those generated by the well-know phonons being the classic lattice excitations. Our results are in good agreement with experimental data and show convincingly that the topological fermion condensation quantum phase transition can be viewed as the universal agent explaining the very unusual physics of strongly correlated Fermi systems.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We report on a new state of matter manifested by strongly correlated Fermi systems including various heavy fermion (HF) metals, two-dimensional quantum liquids such as
3
He films, certain ...quasicrystals, and systems behaving as quantum spin liquids. Generically, these systems can be viewed as HF systems or HF compounds, in that they exhibit typical behavior of HF metals. At zero temperature, such systems can experience a so-called fermion condensation quantum phase transition (FCQPT). Combining analytical considerations with arguments based entirely on experimental grounds, we argue and demonstrate that the class of HF systems is characterized by universal scaling behavior of their thermodynamic, transport, and relaxation properties. That is, the quantum physics of different HF compounds is found to be universal, emerging irrespective of the individual details of their symmetries, interactions, and microscopic structure. This observed universal behavior reveals the existence of a new state of matter manifest in HF compounds. We propose a simple, realistic model to study the appearance of flat bands in two-dimensional ensembles of ultracold fermionic atoms, interacting with coherent resonant light. It is shown that signatures of these flat bands may be found in peculiarities in their thermodynamic and spectroscopic properties. We also show that the FCQPT, in generating flat bands and altering Fermi surface topology, is an essential progenitor of the exotic behavior of the overdoped high-temperature superconductors represented by
La
2
-
x
Sr
x
x
CuO
4
, whose superconductivity differs from that predicted by the classical Bardeen–Cooper–Schrieffer theory. The theoretical results presented are in good agreement with recent experimental observations, closing the colossal gap between these empirical findings and Bardeen–Cooper–Schrieffer-like theories.
Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory ...fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle-hole (C) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity dI/dV, where I is the current and V the bias voltage, is a symmetric function of V. Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn5 and YbRh 2 Si 2 . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition. An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T- and C-invariance, with the differential conductivity again becoming a symmetric function of V. This behavior has been observed in recent measurements of tunneling conductivity in both YbRh 2 Si 2 and graphene. Also within the FC framework, we describe and explain recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that the observed scaling is explained by the emergence of flat bands formed by fermion condensation.
In this brief review, we address manifestations of the
T/B
scaling behavior of heavy-fermion (HF) compounds, where
T
and
B
are the temperature and magnetic field, respectively. Using experimental ...data and the fermion condensation theory, we show that this scaling behavior is typical of HF compounds including HF metals, quasicrystals, and quantum spin liquids. We demonstrate that such scaling behavior holds down to the lowest temperature and field values, so that
T/B
varies in a wide range, provided the HF compound is located near the topological fermion condensation quantum phase transition (FCQPT). Due to the topological properties of FCQPT, the effective mass
M
* exhibits a universal behavior, and diverges as
T
goes to zero. Such a behavior of
M
* has important technological applications. We also explain how to extract the universal scaling behavior from experimental data collected on different heavy-fermion compounds. As an example, we consider the HF metal YbCo
2
Ge
4
, and show that its scaling behavior is violated at low temperatures. Our results obtained show good agreement with experimental facts.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect ...important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence of resistivity in a large number of strongly correlated Fermi systems as well as normal metals. We show that the observed scattering rate is explained by the emergence of flat bands, while the so-called Planckian limit occurs accidentally since the normal metals exhibit the same scattering rate behavior. We also analyze recent challenging experimental data on tunneling differential conductivity collected under the application of magnetic field on the twisted graphene and the archetypical heavy fermion metal YbRh
Si
. Also we describe recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that these observations support the fermion condensation theory. Our theoretical results are in good agreement with corps of different and seemingly unrelated experimental facts. They show that the fermion-condensation quantum phase transition is an intrinsic property of strongly correlated Fermi systems and can be viewed as the universal agent explaining their core physics.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the ...Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage
V
. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of
V
. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of
V
. These findings are in good agreement with recent experimental observations.
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